Hindawi Publishing Corporation
Journal of Energy
Volume 2015, Article ID 384528, 11 pages
http://dx.doi.org/10.1155/2015/384528
Research Article
Midterm Electricity Market Clearing Price Forecasting Using
Two-Stage Multiple Support Vector Machine
Xing Yan and Nurul A. Chowdhury
Department of Electrical Engineering, University of Saskatchewan, Saskatoon, SK, Canada S7N 5A9
Correspondence should be addressed to Xing Yan; [email protected]
Received 31 May 2014; Revised 14 January 2015; Accepted 15 January 2015
Academic Editor: Chuanwen Jiang
Copyright © 2015 X. Yan and N. A. Chowdhury. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Currently, there are many techniques available for short-term forecasting of the electricity market clearing price (MCP), but very
little work has been done in the area of midterm forecasting of the electricity MCP. The midterm forecasting of the electricity
MCP is essential for maintenance scheduling, planning, bilateral contracting, resources reallocation, and budgeting. A two-stage
multiple support vector machine (SVM) based midterm forecasting model of the electricity MCP is proposed in this paper. The first
stage is utilized to separate the input data into corresponding price zones by using a single SVM. Then, the second stage is applied
utilizing four parallel designed SVMs to forecast the electricity price in four different price zones. Compared to the forecasting
model using a single SVM, the proposed model showed improved forecasting accuracy in both peak prices and overall system.
PJM interconnection data are used to test the proposed model.
1. Introduction
Since the generating companies as well as the bulk sellers
want to maximize their profits under a deregulated electricity
market, offering the appropriate amount of electricity at the
right time with the right bidding price is of paramount importance. The forecasting of the electricity price is a prediction
of future electricity price based on given forecast electricity
demand, temperature, sunshine, fuel cost, precipitation, and
other related factors. The electricity market clearing price
(MCP) also called the equilibrium price exists when an
electricity market is clear of shortage and surplus. Once the
electricity MCP is determined, every supplier whose offering
price is below or equal to the electricity MCP will be picked
up to supply electricity at that hour. To ensure fairness of
the market and to avoid market manipulation, the picked up
suppliers will be paid at the electricity MCP, not the price they
offered.
Currently, in the electricity price forecasting studies,
short-term forecasting of the electricity MCP is the most
focused research area. It is also commonly known as the 24hour day-ahead electricity price forecasting. Unlike the shortterm forecasting, very little work has been done to forecast
electricity MCP on a midterm basis [1–5]. The midterm
forecasting of the electricity MCP focuses on a time frame
from one month to six months. It is essential for decision
making and midterm planning purposes such as generation
plant expansion and maintenance schedule, reallocation of
resources, bilateral contracts, and hedging strategies [5]. The
midterm forecasting of the electricity MCP is different from
the short-term forecasting in many ways. First of all, midterm
forecasting by its nature cannot utilize the trend from the
immediate past while the short-term forecasting can. Future
segment is not contiguous to the immediate past history for
which electricity MCP data are available for the midterm
forecasting of the electricity MCP. In order to accurately
forecast the future electricity MCP with segmented input
data, the midterm forecasting model must possess very strong
adaptability in handling out-of-sample and segmented data
during training phase. Secondly, because of the unavailability
of immediate past data, forecasting technique such as time
series cannot be utilized in midterm forecasting. In midterm
electricity price forecasting, each input data at hour 𝑡 has
to be treated independently from its nearby data such as
𝑡 − 𝑛 or 𝑡 + 𝑛, for 𝑛 equals 1, 2, 3, . . .. Moreover, locating
and predicating peak prices in the midterm forecasting of
the electricity MCP are extremely difficult. As the shortterm forecasting can utilize the trend from the immediate
2
past, locating the peak prices in most cases is usually very
accurate. The main challenge in short-term forecasting is how
accurately the forecasting model can predict the values at
each peak price spot. However, in the midterm forecasting
of the electricity MCP, because of the unavailability of data
from the immediate past, locating the peak prices becomes
extremely difficult. As a result, accurately predicting the
values at peak price spots becomes even more difficult.
The fourth difference is the length of historical data that
are needed to train the forecasting model. The short-term
forecasting of the electricity price model usually only needs
the data of the last couple of days to train the forecasting
model. On the other hand, the midterm forecasting model
requires one year of historical data in order to train the
forecasting model. Finally, only nonlinear regression based
forecasting models are capable of midterm forecasting. Linear
regression based forecasting models can only be considered
as an add-on module in the midterm forecasting.
Before hybrid models utilized in the forecasting of the
electricity MCP, autoregressive integrated moving average
(ARIMA) [6], wavelet transform [7–9], Monte Carlo simulation [10], bid-based stochastic model [10], time series
[11, 12], and dynamic regression [13] are the first generation
of techniques utilized in the forecasting of the electricity
MCP. Artificial neural network (ANN) was later on applied
to forecast short-term electricity MCP [2–4, 14–19] because
of its flexibility in handling highly nonlinear relationships
and relatively easy implementation. PJM interconnection,
Australian electricity market, England-Wales pool, and New
England ISO [16] are currently utilizing ANN to forecast the
electricity MCP.
Support vector machine (SVM) is a new learning method
based on structural risk minimization and has gained
increased attention in recent electricity price forecasting [20–
23] studies. The major advantages of SVM over ANN or any
other forecasting models are that SVM can avoid problems
such as data overfitting, local minimum, and unpredictably
large out-of-sample data error while at the same time still
achieving better results. SVM is also a very robust forecasting
model and will always end up with the same acceptable
result regardless of the initial values. On top of that, SVM
has less adjustable parameters compared to ANN and is
less complicated in control parameter selection. In electricity
price forecasting, a traditional SVM can achieve around 3%
[24] improved forecasting accuracy compared to a traditional
ANN. Several algorithms including genetic algorithm (GA)
[24–27], artificial fish swarm algorithm [28], independent
component analysis (ICA) algorithm [29, 30], and rough sets
algorithm [31, 32] are used to further optimize the training
of SVM. Moreover, the least squares support vector machine
(LSSVM) was later developed to improve the accuracy of the
original SVM [25, 27, 33–35]. Although each method has
shown some improvements, the overall system accuracy was
still quite low.
The new trend in recent short-term forecasting of the
electricity price studies is using hybrid models combining
several prediction methods. Hybrid models can compensate
the weaknesses of utilizing any individual established method
and achieve better overall system results. Torghaban et al. [5]
Journal of Energy
proposed hybrid midterm electricity monthly average price
forecasting models combined with SVM/SVM, SVM/NN,
NN/SVM, and NN/NN. Swief et al. [23] utilized the principle
component analysis (PCA) and 𝑘 nearest neighbor (𝑘NN)
points technique to reduce the number of data entries to the
SVM model. Wang and Qin [32] introduced an electricity
price prediction model using rough sets and SVM where
the rough sets theory was used to simplify the SVM input
variables. Xie et al. [33] proposed a hybrid electricity price
forecasting model that integrates clustering algorithm with
LSSVM. Fan et al. [35] proposed a hybrid forecasting model
that includes the Bayesian clustering by dynamics (BCD)
and SVM where the BCD classifier is applied to cluster
the input data set into several subsets in an unsupervised
manner. Zhao et al. [36] forecasted the prediction interval
of the electricity price utilizing SVM and nonlinear conditional heteroscedastic forecasting (NCHF) model. They
also proposed a hybrid model [37, 38] using SVM and
probability classifier to predict the price spike occurrence
and values. Areekul et al. [39] proposed forecast techniques
based on autoregressive integrated moving average (ARIMA)
and ANN. Xie et al. [40] proposed a sensitivity analysis of
electricity price utilizing SVM and regression model where
several price-load elasticity equations are built based on the
price pattern data sets classified by SVM classification. A
similar work focused on price-load elasticity analysis is done
by Wang in [41]. Pousinho et al. [42] proposed a hybrid
short-term electricity price forecasting model combined with
particle swarm optimization (PSO) and adaptive-network
based fuzzy inference system (ANFIS).
A new midterm forecasting model of the electricity
MCP utilizing two-stage multiple SVM is proposed in this
paper based on the studying of previous works in midterm
forecasting of the electricity MCP shown in Table 1. The
proposed model can predict both patterns and values of
electricity MCP. A single SVM is first used to separate the
input data into corresponding price zones. Then, four parallel
designed SVMs are used to forecast the price values inside
each separated price zone. The main contributions of this
paper include (1) addressing and resolving problems associated with midterm forecasting of the electricity MCP, (2)
addressing and resolving the problems associated with using
a single nonlinear forecasting model to forecast midterm
electricity MCP, such as SVM, and (3) presenting a twostage multiple SVM based forecasting model. Experimental
results using historical data from the PJM interconnection
system demonstrated that the proposed two-stage multiple
SVM forecasting model can improve the price predicting
accuracy in both low and peak price zones. The rest of
the paper is organized as follows. Two-stage multiple SVM
based midterm forecasting model of the electricity MCP is
given in Section 2. Case studies are presented in Section 3.
Conclusions are included in Section 4.
2. Two-Stage Multiple SVM Based Midterm
Forecasting Model of the Electricity MCP
2.1. Support Vector Machine. SVM was first introduced by
Vladimir Vapnik in 1979 based on the statistical learning and
Journal of Energy
3
Table 1: Comparison of previously published midterm forecasting techniques of electricity prices.
Authors
Forecasting objectives and techniques
Midterm forecasting of the monthly
average electricity spot prices using
various techniques
Midterm forecasting of the electricity
hourly MCP utilizing ANN technique
Midterm forecasting of the monthly
average electricity spot prices utilizing
linear forecasting models
Midterm forecasting of the electricity
hourly MCP utilizing hybrid LSSVM
and ARMAX techniques
Strengths
Pedregal and
Trapero [44]
Midterm forecasting of the electricity
hourly price utilizing unobserved
component models
Utilization of numbers framed
short-term forecast results to
serve in the midterm forecasting
González et al. [45]
Midterm forecasting of electricity hour
price utilizing hybrid approaches
based on the analysis between market
price and marginal costs
Forecast the real price based on
adjusting the prediction values of
the marginal price forecasting
Torbaghan et al. [1]
Yan [2], Yan and
Chowdhury [3, 4]
Torghaban et al. [5]
Yan and
Chowdhury [43]
X = [x1 , x2 , . . . , xN ]
x1
x2
K(x, xi )
Bias
K(x, xi )
..
.
..
.
∑
Output neuron
xN
N inputs
K(x, xi )
Hidden layer
Figure 1: SVM architecture [36].
Both single and hybrid models
are tested
Extended training data set
Dummy variables are considered
in the model indicating
seasonality during simulation
The proposed hybrid model is
capable of adjusting the errors
from the previous module
Weaknesses
Only focused on the monthly
average electricity spot prices
(only 12 outputs)
Poor performance in forecasting
peak prices
Only focused on the monthly
average electricity spot prices
(only 12 outputs)
Limited improvements in
forecasting peak prices
The proposed model is compared
with an ARIMA model which
has quite weak performance in
midterm forecasting
Only price data is involved in the
proposed study and the forecast
of the marginal price is under an
ideal electricity market
layer connecting the input layer and the output layer. Kernels
transfer low dimensional input data vector into a much higher
dimensional vector (sometime can be infinite) and eventually
transfer the highly nonlinear problem inside the input space
into a linear problem inside the feature space. After the
transformation is completed, optimization algorithms are
then applied in order to perform the regression or classification computation. SVM uses a quadratic formulation as
optimization algorithm.
Suppose that {(𝑋𝑡 , 𝑦𝑡 )} for 𝑡 = 1 to 𝑁 is a given set of
data, where 𝑋𝑡 = (𝑥𝑡1 , 𝑥𝑡2 , . . . , 𝑥𝑡𝑘 ) is the input vector at time
𝑡 with 𝑘 elements and 𝑦𝑡 is the corresponding price data at
time 𝑡 which could be defined as
𝑦𝑡 = 𝑓 (𝑋𝑡 ) = ⟨𝑊, 𝜑 (𝑋𝑡 )⟩ + 𝑏,
later on developed by Vladimir Vapnik and his coworkers
at the AT&T Bell Laboratories in 1995. After the book An
Introduction of Support Vector Machines and Other KernelBased Learning Methods by Nello Cristianini and John ShaweTaylor published in 2000, it started getting more popularity
and application in many fields. At the early stage, SVM was
only used for classification purposes. Then, the regression
computation of nonlinear function was added by solving a
convex quadratic optimization problem [46].
A brief SVM architecture is shown in Figure 1. It is
very similar to a 3-layer feed-forward ANN. It has the
input and output layers containing either single or multiple
input/output data. The only difference is inside the hidden
layer where kernels replace the hidden neurons. The working
principle of a SVM is also different from that of an ANN.
A 3-layer feed-forward ANN contains two transfer functions
connecting the input layer to the hidden layer and the hidden
layer to the output layer. SVM, on the other hand, only
has kernels acting like transfer functions inside the hidden
(1)
where ⟨, ⟩ denotes the dot product, 𝑊 is the weight vector, 𝑏
is the bias, and 𝜑() is the mapping function transfers input
vector 𝑋𝑡 into a much higher dimensional feature space
(could be infinite). The corresponding optimization problem
is then
minimize
𝑁
1
‖𝑊‖2 + 𝐶 ∑ (𝜉𝑡 + 𝜉𝑡∗ ) ,
2
𝑡=1
subject to
𝑦𝑡 − ⟨𝑊, 𝜑 (𝑋𝑡 )⟩ − 𝑏 ≤ 𝜀 + 𝜉𝑡 ,
⟨𝑊, 𝜑 (𝑋𝑡 )⟩ + 𝑏 − 𝑦𝑡 ≤ 𝜀 +
(2)
𝜉𝑡∗ ,
𝜉𝑡 , 𝜉𝑡∗ ≥ 0,
where 𝐶 is the regularization constant with regard to the unit
cost of errors. 𝜉𝑡 and 𝜉𝑡∗ are the slack variables measuring the
cost of the errors both above and below the target value in
4
Journal of Energy
the training points. The 𝜀-insensitive loss function with 2𝜀
bandwidth is defined as
󵄨
󵄨
0,
if 󵄨󵄨󵄨𝑦𝑡 − 𝑓 (𝑋𝑡 )󵄨󵄨󵄨 ≤ 𝜀
󵄨
󵄨󵄨
󵄨󵄨𝑦𝑡 − 𝑓 (𝑋𝑡 )󵄨󵄨󵄨𝜀 = {󵄨󵄨
󵄨󵄨
󵄨󵄨𝑦𝑡 − 𝑓 (𝑋𝑡 )󵄨󵄨 − 𝜀, otherwise.
(3)
When adding the Lagrange multipliers to (2), the problem
can be rewritten as
𝐿 (𝑊, 𝜉, 𝜉∗ , 𝛼, 𝛼∗ , 𝜂, 𝜂∗ )
=
𝑁
− ∑ 𝛼𝑡 (𝜀 + 𝜉𝑡 − 𝑦𝑡 + ⟨𝑊, 𝜑 (𝑋𝑡 )⟩ + 𝑏)
𝑡=1
−
∑ 𝛼𝑡∗
𝑡=1
(𝜀 +
𝜉𝑡∗
(4)
+ 𝑦𝑡 − ⟨𝑊, 𝜑 (𝑋𝑡 )⟩ − 𝑏)
(7)
𝜂𝑡∗ 𝜉𝑡∗ = (𝐶 − 𝛼𝑡∗ ) 𝜉𝑡∗ = 0.
𝑏 = 𝑦𝑡 − ⟨𝑊, 𝜑 (𝑋𝑡 )⟩ ± 𝜀
for 𝛼𝑡 , 𝛼𝑡∗ ∈ [0, 𝐶] .
(8)
𝑁
A modified version of (9) can be expressed as
where 𝛼𝑡 , 𝛼𝑡∗ , 𝜂𝑡 , and 𝜂𝑡∗ are the Lagrange multipliers. The
partial derivates of the Lagrange function with the primal
variables (𝑊, 𝑏, 𝜉𝑡 , and 𝜉𝑡∗ ) are then
𝑁
𝜕𝐿 SVM
= 0 󳨀→ 𝑊 = ∑ (𝛼𝑡 − 𝛼𝑡∗ ) 𝜑 (𝑋𝑡 ) ,
𝜕𝑊
𝑡=1
𝜕𝐿 SVM
= 0 󳨀→ ∑ (𝛼𝑡 − 𝛼𝑡∗ ) = 0,
𝜕𝑏
𝑡=1
𝜕𝐿 SVM
= 0 󳨀→ 𝐶 − 𝛼𝑡∗ − 𝜂𝑡∗ = 0.
𝜕𝜉𝑡∗
The dual problem can be obtained by substituting the relations from (5):
1 𝑁
∑ (𝛼 − 𝛼𝑡∗ ) (𝛼𝑙 − 𝛼𝑙∗ ) ⟨𝜑 (𝑋𝑡 ) , 𝜑 (𝑋𝑙 )⟩
2 𝑡,𝑙=1 𝑡
𝑁
𝑡=1
𝑡=1
(10)
𝑡=1
where 𝐾(𝑋, 𝑋𝑡 ) = ⟨𝜑(𝑋), 𝜑(𝑋𝑡 )⟩ is called the kernel function.
Gaussian radial basis kernel (11) is the most powerful one in
nonlinear function estimation:
(11)
(5)
𝜕𝐿 SVM
= 0 󳨀→ 𝐶 − 𝛼𝑡 − 𝜂𝑡 = 0,
𝜕𝜉𝑡
𝑁
𝑁
𝑦𝑡 = 𝑓 (𝑋𝑡 ) = ∑ (𝛼𝑡 − 𝛼𝑡∗ ) 𝐾 (𝑋, 𝑋𝑡 ) + 𝑏,
󵄩2
󵄩󵄩
󵄩󵄩𝑋 − 𝑋𝑡 󵄩󵄩󵄩
).
𝐾 (𝑋, 𝑋𝑡 ) = exp (−
2𝜎2
𝑁
− 𝜀 ∑ (𝛼𝑡 + 𝛼𝑡∗ ) + ∑ 𝑦𝑡 (𝛼𝑡 − 𝛼𝑡∗ ) ,
𝑁
∑ (𝛼𝑡 − 𝛼𝑡∗ ) = 0,
𝑡=1
𝛼𝑡 , 𝛼𝑡∗ ∈ [0, 𝐶] .
(9)
𝑡=1
𝑡=1
subject to
𝜂𝑡 𝜉𝑡 = (𝐶 − 𝛼𝑡 ) 𝜉𝑡 = 0,
𝑦𝑡 = 𝑓 (𝑋𝑡 ) = ∑ (𝛼𝑡 − 𝛼𝑡∗ ) ⟨𝜑 (𝑋) , 𝜑 (𝑋𝑡 )⟩ + 𝑏.
− ∑ (𝜂𝑡 𝜉𝑡 + 𝜂𝑡∗ 𝜉𝑡∗ ) ,
−
𝛼𝑡∗ (𝜀 + 𝜉𝑡∗ + 𝑦𝑡 − ⟨𝑊, 𝜑 (𝑋𝑡 )⟩ − 𝑏) = 0,
The final SVM for nonlinear functions can be written as
𝑁
maximize
𝛼𝑡 (𝜀 + 𝜉𝑡 − 𝑦𝑡 + ⟨𝑊, 𝜑 (𝑋𝑡 )⟩ + 𝑏) = 0,
The above equations indicate that for all samples whose
Lagrange multipliers are equal to zero are considered as
nonsupport vectors. Samples with nonzero coefficients are
considered as support vectors. Meanwhile, 𝑏 can be calculated
when the slack variables 𝜉𝑡 and 𝜉𝑡∗ are equal to zero
𝑁
1
‖𝑊‖2 + 𝐶 ∑ (𝜉𝑡 + 𝜉𝑡∗ )
2
𝑡=1
𝑁
will vanish at the optimal solution. This gives the following
equations:
2.2. Price Zones Analysis. One of the special characteristics
of electricity is that it has to be produced as used. Taking PJM interconnected electricity market as an example,
electricity price can vary from as low as –$10/MWh to as
high as $748/MWh [30]. The relationship between supply
and demand under normal deregulated market is no longer
the only dominant principle determining the electricity
price. Other factors such as business competing strategy
and unethical business behaviour are heavily involved and
cannot be efficiently simulated. Therefore, the accuracy of the
forecasted electricity MCP in the peak price zone is always
very low. Although electricity MCP is very volatile, it is still
normally distributed along its average value [20–22]. In the
proposed work, the electricity MCP is separated into four
price zones: low, medium, high, and peak price zones. Let
𝜇 and 𝜎 be the mean and standard deviation of the monthly
historical electricity MCP; the four price zones of each month
are determined based on the four criteria listed below:
low: MCP < 𝜇 − 𝜎;
(6)
According to the Karush-Kuhn-Tucker (KKT) conditions, the
terms inside the equation containing the Lagrange multipliers
medium: 𝜇 − 𝜎 ≤ MCP < 𝜇 + 0.5𝜎;
high: 𝜇 + 0.5𝜎 ≤ MCP < 𝜇 + 1.5𝜎;
peak: 𝜇 + 1.5𝜎 ≤ MCP.
Journal of Energy
About 15%–25% of the price is in the low price zone.
50%–60% of the price is in the medium price zone. 15%
−20% of the price is in the high price zone. Finally, the last
5%–10% of the price will be in the peak price zone. The
standard deviation multipliers are chosen based on the price
characteristics of the PJM interconnected electricity market
and forecasting model parameter optimization. They can be
modified when applying in a different electricity market.
Inside the medium price zone, most generating companies
are participating in supplying electricity. Every participating
generating unit is running at its optimal output. There is
plenty of reserved energy available in the market which can
be supplied immediately. Congestion is low in most areas
and congestion cost is limited. At this moment, the market
is at its stable state. Sudden shortage or surplus can be easily
recovered or offset by other generating companies in the same
and nearby jurisdiction. Supply and demand elasticity plays
a major role and electricity MCP is mainly determined by
the demand and fuel cost. Inside the low price zone, the
profit margin is small and, therefore, only companies with
low production cost and mandatory all-time running power
units such as nuclear power plants are participating. Sudden
shortage or surplus could cause price spikes because they
cannot be recovered or offset as easily as in the medium price
zone. In the peak price zone, most power plants are running
at their peak capacity. Transmission lines are under extreme
load resulting in extremely high congestion cost in some
areas. System reserved energy is very low and generating
companies expect to take advantages and make huge profits
from it. Electricity MCP is mainly determined by business
competing strategy and even unethical business behaviour
in the peak price zone. The high price zone is between
the medium and peak price zones and, therefore, shows
characteristics of both price zones. The supply and demand
relationship and business competing strategy both dominate
the final electricity MCP inside the high price zone.
2.3. Two-Stage Multiple SVM Forecasting Model Architecture.
The architecture of the proposed two-stage multiple SVM
based midterm forecasting model of the electricity MCP is
shown in Figure 2. It contains four layers: (1) input layer, (2)
input data distribution layer, (3) SVM price prediction layer,
and (4) output layer.
Inside the input layer, there will be input data such as
electricity hourly demand, electricity daily peak demand, and
daily natural gas price. Data selection and preprocessing will
be explained in detail in Section 2.4. After all the data are
preprocessed inside the input layer, a single SVM is first
utilized to predict the initial values of the electricity prices.
These price values are then separated into four predefined
price zones: low, medium, high, and peak. The input data
distribution layer can significantly reduce the range each
price prediction SVM shall cover and improve the overall
system accuracy when forecasting the midterm electricity
MCP. After the input data distribution is completed, the
SVM prediction module is utilized to forecast the midterm
electricity MCP. There are four parallel connected SVMs
inside the price prediction module to forecast the electricity
MCP in four different price zones. Based on the different
5
Peak price
SVM
Input
data
X1
X2
SVM
Price
zones
initial
forecasting separation
High price
SVM
Output
..
.
Medium price
SVM
Xn
Low price
SVM
Figure 2: Two-stage multiple SVM forecasting model architecture.
range of input data, each price prediction SVM optimizes its
own control parameters during the training process. These
different control parameters give each price prediction SVM
the ability to capture the characteristics between input and
output data within each price zone. Inside the output layer,
four SVMs predicted electricity price values are combined to
form the final forecast electricity MCP. Input data distribution module will assign each input data with serial numbers
that will be used to regroup all forecast price values from
the SVM price prediction layer inside the output layer. The
training input data for both modules are from the input
layer in Figure 2. The target data for both modules are
the historical electricity MCP. Cross-validation technique is
applied in data distribution and price prediction modules for
the optimization of the control parameters.
2.4. Data Collection and Preprocessing. Electricity MCP can
be forecasted by evaluating a variety of elements [31] such
as electricity demand, supply, natural gas price, coal price,
hydrocapacity, weather, and temperature. An ideal forecasting model of the electricity MCP should include all the
possible elements that affect the final electricity MCP. In
reality, however, it is impossible and unnecessary to do so.
Since weather conditions including daily temperature are
already considered in load forecasting, they do not have to be
included in MCP forecasting process. Other elements such
as business strategy and unethical competition behaviours
cannot be easily represented mathematically. Finally, the
current failure or operating status of a generator in many
deregulated electric market is confidential information. Due
to the factors mentioned above, a data selection process is
presented in Figure 3 using cross-validation technique to
finalize the input data that were taken into account for the
proposed work.
The data selection process starts with only the default
input data (hourly electricity demand) inside the forecasting
model. Then, the next element inside the potential input
data is added to the initial forecasting model to test whether
the added element improves the forecasting accuracy or not.
Tested element will be added to the forecasting model if it
improves the forecasting accuracy. Otherwise, the forecasting
model maintains its current input data and the next element
inside the potential input data will be tested. Due to the
fact that sometimes adding more than one element at a time
6
Journal of Energy
Potential input data
Move on to
the next
combination
Forecasting model with hourly
demand. Does the added input
data improve the forecasting
accuracy? (yes/no)
Yes
No
No
Move on to
the next
input data
New input data
added to the model
Is this the last possible
combination of the potential
input data? (yes/no)
Yes
Cross-validation on input data
selection is completed
Figure 3: Data selection process.
will achieve better forecasting results, different combinations
of elements will also be tested once all the elements have
been tested one at a time. By applying the data selection
process shown in Figure 3, it will guarantee to test not only
every single element but also every possible combination
of elements that would lead to the optimized forecasting
results. The final selected input data for the proposed twostage multiple SVM forecasting model at each hour 𝑡 include
(1) electricity hourly demand at hour 𝑡, (2) electricity daily
peak demand, (3) electricity monthly average demand, (4)
daily price of natural gas, (5) previous year’s monthly average
electricity MCP, (6) month (1–12), and (7) hour of the day (1–
24). The target data at hour 𝑡 is the electricity MCP at hour 𝑡.
Moreover, one year is the most optimized length of historical
data to train the forecasting model based on the previous
published works [1–3] regarding the selection of training data
for midterm forecasting of the electricity MCP.
Part of the training data is separated from the rest of the
training data and served as the so-called the testing data.
The testing data are used to optimize the control parameters
of the proposed forecasting model and are treated unseen
from the rest of the training data. For the rest of this paper,
the remaining part of the training data is called the actual
training data. In the proposed work, data from January 1,
2009, to December 31, 2009, excluding June 2009, are selected
as the actual training data and can be viewed as a matrix
with 8040 (24 × 335) rows and 8 columns. The 8040 rows
are the number of hours from hour 1 (1:00 a.m.) on January 1,
2009, to hour 24 (12:00 a.m.) on December 31, 2009, excluding
June 2009. The first 7 columns are the 7 input elements
mentioned before. The last column is the training target data,
electricity MCP from hour 1 (1:00 a.m.) on January 1, 2009,
to hour 24 (12:00 a.m.) on December 31, 2009, excluding
June 2009. Because the proposed two-stage multiple SVM
based midterm forecasting model of the electricity MCP is
designed to predict the 720 hourly electricity MCPs in June
2010, selecting data from hour 1 (1:00 a.m.) on June 1, 2009, to
hour 24 (12:00 a.m.) on June 30, 2009, as the testing data could
create the best scenarios on daily demand pattern, daily price
pattern, weather, sunshine, and precipitation during training
process to optimize the control parameters. For the same
reason, if the proposed model is utilized to forecast the 744
hourly electricity MCPs in May 2010, data in May 2009 will
be selected as the testing data during training process. The
testing data contain a matrix with 720 rows (24 × 30) and 8
columns. The first 7 columns are the testing input data and
the last column is the testing target data.
Once the training procedure is done, the proposed twostage multiple SVM forecasting model is used to forecast the
midterm electricity MCP of every hour in June 2010 using
historical data from January 2009 to December 2009. This
work is based on the assumption that all forecasting input
data have already been accurately predicted to limit the affects
from inaccurate input data. The forecast output contains
720 (24 × 30) hourly electricity MCP which will insure the
comprehensiveness of the test sample. The forecasting input
data could be viewed as a matrix with 720 (24 × 30) rows and
8 columns. The 720 rows are the number of hours from hour 1
(1:00 a.m.) on June 1, 2010, to hour 24 (12:00 a.m.) on June 30,
2010. The first 7 columns are the forecasting input data and
the last column is the electricity MCP from hour 1 (1:00 a.m.)
on June 1, 2010, to hour 24 (12:00 a.m.) on June 30, 2010.
In order to improve the regression accuracy and avoid
the dominance of some extremely large values inside the data
set, data preprocessing is needed in machine learning. For
electricity MCP forecasting, the most common and recommended data preprocessing algorithms are the normalization.
Normalization converts each datum inside its corresponding
element into a value between –1 and +1 (sometimes between
0 and 1) with respect to each element’s maximum and minimum value. Depending on the calculation, the maximum and
minimum values can be either global or local. Suppose that
𝑋𝑡 = (𝑥𝑡1 , 𝑥𝑡2 , . . . , 𝑥𝑡𝑘 ) is a given set of vectors at time 𝑡 with
𝑘 multiple elements for 𝑡 = 1 to 𝑁. The normalization for
datum 𝑥𝑡𝑘 could be defined as
𝑥̂𝑡𝑘 =
𝑥𝑡𝑘 − (𝑥MAX𝑘 + 𝑥MIN𝑘 ) /2
,
𝑥MAX𝑘 − (𝑥MAX𝑘 + 𝑥MIN𝑘 ) /2
(12)
where 𝑥MAX𝑘 and 𝑥MIN𝑘 are the global or local maximum and
minimum values inside the 𝑘th element. The normalization
on forecasting input data is performed using each element’s
corresponding global or local maximum and minimum
values during the training process. The target data remain
unchanged as there is only the electricity MCP data. The
designed two-stage multiple SVM based midterm forecasting
model of the electricity MCP can utilize different dimensions
of input data for forecasting accuracy optimization. The full
dimension of the input data is 7 as mentioned before. Recall
the data selection process from Figure 3 and, using mean
absolute error for the performance evaluation, the optimized
final dimensions of input data for the proposed multiple SVM
are 7 for the initial prediction SVM, 5 for the low price SVM,
7 for the medium price SVM, 7 for the high price SVM, and
7 for the peak price SVM.
2.5. Performance Evaluation. Mean absolute error (MAE),
mean absolute percentage error (MAPE), and mean square
root error (MSRE) are the three most widely used measurements for performance evaluation in forecasting electricity
price values. Given 𝑁 historical electricity MCP data, 𝑦𝑡 , and
Journal of Energy
7
1 𝑁󵄨
󵄨
MAE = ∑ 󵄨󵄨󵄨𝑦𝑡 − 𝑦̂𝑡 󵄨󵄨󵄨 ,
𝑁 𝑡=1
󵄨󵄨 𝑦 − 𝑦̂ 󵄨󵄨
1
󵄨
𝑡 󵄨󵄨
MAPE =
∑ 󵄨󵄨󵄨 𝑡
󵄨 × 100%,
𝑁 𝑡=1 󵄨󵄨 𝑦𝑡 󵄨󵄨󵄨
𝑁
(13)
1 𝑁
2
MSRE = √ ∑ (𝑦𝑡 − 𝑦̂𝑡 ) .
𝑁 𝑡=1
During the training process, two SVM control parameters,
the coefficient of the Gaussian radial basis kernel 𝜎 and
the regularization constant 𝛾, are set at an initial value and
updated using testing data during each iteration until the
MAE of the SVM reaches its global minimum. Once all
control parameters are determined, forecasting input data can
be applied to forecast the midterm electricity MCP.
3. Case Studies
3.1. PJM Interconnected Electric Market. PJM interconnected
electric market is the largest interconnected system in the
world. It includes all or most of Delaware, District of
Columbia, Maryland, New Jersey, Ohio, Pennsylvania, Virginia, and West Virginia. Parts of Indiana, Illinois, Kentucky,
Michigan, North Carolina, and Tennessee are also included
in the PJM interconnected electric market. The market serves
more than 61 million people in the United States. As of
December 31, 2012, it had an installed generating capacity of
183,604 megawatts and more than 800 participating members. The market covered 243,417 square miles of territory
containing 62,556 miles of transmission lines and more
than 1,376 electric generators [47]. Coal (74%) and natural
gas (22%) are the two major types of fuel in the market.
Locational marginal pricing (LMP) is used to reflect the value
of the energy at the specific location and time it is delivered.
The market consists of day-ahead and real-time markets. The
day-ahead market is a forward market in which hourly LMP
is calculated for the next operating day based on generation
offers, demand bids, and scheduled bilateral transactions. The
real-time market is a spot market in which current LMP
is calculated at five-minute intervals based on actual grid
operating conditions. PJM settles transactions hourly and
issues invoices to market participants monthly [48]. The LMP
inside the PJM interconnected electric market is used as
electricity MCP in this work. Historical data from the dayahead market of 2008 and 2009 are used in this work to
forecast the electricity MCP in June 2010 and are available at
[47].
3.2. Experimental Results. The testing results using both
single SVM and the proposed two-stage multiple SVM are
shown in Figure 4. Data from January 2009 to December
2009 excluding June 2009 are used as the actual training data
and data in June 2009 are used as the testing data.
It can be seen that the major contribution of utilizing
a two-stage multiple SVM based forecasting model is the
80
Electricity MCP ($/MWh)
the corresponding forecasted price data 𝑦̂𝑡 for 𝑡 = 1 to 𝑁,
MAE, MAPE, and MSRE are defined as
70
60
50
40
30
20
10
0
100
200
300
400
Hour
500
600
700
Real MCP
Single SVM forecast MCP
Two-stage multiple SVM forecast MCP
Figure 4: Forecasted electricity MCP in June 2009 using both single
and two-stage multiple SVM.
Table 2: Performance evaluation results of MAE between the single
and the two-stage multiple SVM in June 2009.
MAE
Single
Multiple
PRIM
Low
4.0094
3.1985
20.22%
Medium
1.8941
1.8678
1.39%
High
3.0837
3.8336
−24.32%
Peak
8.2403
5.7636
30.06%
System
2.9743
2.9625
0.40%
Table 3: Performance evaluation results of MAPE between the
single and the two-stage multiple SVM in June 2009.
MAPE
Single
Multiple
PRIM
Low
35.9821
24.9639
30.62%
Medium
6.1526
5.6042
8.91%
High
7.2207
8.7352
−20.97%
Peak
14.5750
11.2517
22.80%
System
11.7491
11.4083
2.90%
improved forecasting results in the low and peak price zones.
The regression computation performance evaluations are
performed using MAE, MAPE, and MSRE analyses. The performance numbers are shown in Tables 2, 3, and 4. Percentage
improvement (PRIM) is used to compare the regression
computation performance between the single SVM model
and the proposed two-stage multiple SVM model. The PRIM
is calculated as
PRIM = ((single MAE/MSRE/MAPE
− multiple MAE/MSRE/MAPE)
(14)
−1
⋅ (single MAE/MSRE/MAPE) ) × 100%.
Positive PRIM values indicate that the two-stage multiple
SVM model is better than the single SVM model in this price
zone. Negative PRIM values indicate the opposite.
According to all three tables, MAE, MAPE, and MSRE
values show that the two-stage multiple SVM model is more
accurate than the single SVM model by more than at least
20% in the low and peak price zones. However, the results
8
Journal of Energy
Table 4: Performance evaluation results of MSRE between the single
and the two-stage multiple SVM in June 2009.
Table 6: Performance evaluation results of MAPE between the
single and the two-stage multiple SVM in June 2010.
MSRE
Single
Multiple
PRIM
MAPE
Single
Multiple
PRIM
Low
0.5200
0.3381
34.98%
Medium
0.1191
0.1408
−18.22%
High
0.2933
0.3590
−22.40%
Peak
1.2738
1.0060
21.02%
System
0.1564
0.1536
1.79%
Low
21.0094
10.2069
51.42%
Medium
16.3663
18.9028
−15.50%
High
7.5146
12.4708
−65.95%
Peak
16.7736
12.0534
28.14%
System
15.6454
14.6567
6.32%
Table 5: Performance evaluation results of MAE between the single
and the two-stage multiple SVM in June 2010.
Table 7: Performance evaluation results of MSRE between the single
and the two-stage multiple SVM in June 2010.
MAE
Single
Multiple
PRIM
MSRE
Single
Multiple
PRIM
Low
5.7523
2.7764
51.73%
Medium
6.9711
7.5398
−8.16%
High
5.0316
7.6556
−52.15%
Peak
15.9496
11.1233
30.26%
System
7.2523
6.8106
6.09%
are opposite in the high price zones. This is caused by the
characteristics of the high price zone as it is between the
medium and peak price zones. The supply and demand
relationship and business competing strategy both dominate
the final electricity MCP inside the high price zone. It is very
difficult for a single SVM to simulate these two very different
characteristics at the same time. Significantly reduced data
caused by the SVM classification process is also another
reason; MAE, MAPE, and MSRE are low in the high price
zone. As the MSRE values in the medium price zones are
opposite compared to the MAE and MAPE values, it is
hard to say which model has the better performance in the
medium price zone. Usually, the conclusions obtained from
the performance numbers of MAE, MAPE, and MSRE should
be identical. However, in special cases, the conclusions would
differ from each other due to the different distribution of
results. For instance, suppose that the forecasting errors from
the single SVM and two-stage multiple SVM are (6, 6) and (1,
10) and the forecasting percentage errors from the single SVM
and two-stage multiple SVM are (6%, 6%) and (1%, 10%).
The size of the data set is only 2. Therefore, the MAE of the
single SVM and the two-stage multiple SVM are (6 + 6)/2 =
6 and (1 + 10)/2 = 5.5. According to the MAE values, the twostage multiple SVM is better than the single SVM. The same
conclusions apply to the MAPE evaluation where the MAPEs
of the single SVM and the two-stage multiple SVM are (6%
+ 6%)/2 = 6% and (1% + 10%)/2 = 5.5%. However, when
comparing the MSRE values, the conclusion is different. The
MSREs of the single SVM and the two-stage multiple SVM
are (62 + 62 )0.5 /2 = 4.243 and (12 + 102 )0.5 /2 = 5.025. According
to the MSRE values, the single SVM is better than the twostage multiple SVM. Under special situation like this, when
the conclusions obtained by the MAE, MAPE, and MSRE
values do not agree with each other in certain price zones
(e.g., the medium zone), because all the control parameters
are determined based on the global minimal MAE values,
we will use the MAE values to determine which forecasting
model is better.
As the testing results supported the fact that the twostage multiple SVM is better than the single SVM in midterm
forecasting of the electricity MCP, the proposed forecasting
model is used to forecast the midterm hourly electricity
Low
0.4572
0.2569
43.81%
Medium
0.3350
0.4872
−45.43%
High
0.5299
0.6411
−20.99%
Peak
2.6890
1.7935
33.30%
System
0.3316
0.3126
5.73%
MCP in June 2010 using historical data from January 2009
to December 2009. Figure 5 shows the forecast electricity
hourly MCP in June 2010 using both single and the two-stage
multiple SVM. The final midterm forecasting results of the
electricity hourly MCP are obtained from the combination
of predicted price from four price prediction SVMs. Detailed
evaluation results of MAE, MAPE, and MSRE are shown in
Tables 5, 6, and 7. The two-stage multiple SVM forecasting
model shows an average 6% improvement on the system
MAE, MAPE, and MSRE evaluations. The negative PRIM
values in the high price zone are expected while the negative
PRIM values in the medium price zone indicate that there is
misdistribution during the forecast process. The forecasting
results of the proposed multiple SVM model are also compared with other machine learning methods [43] shown in
Table 8. Although the proposed two-stage multiple SVM is
only slightly better in forecasting accuracy compared with
other midterm electricity MCP forecasting methods such
as the hybrid LSSVM and ARMAX during the forecasting
process, the proposed two-stage multiple SVM model is
way more flexible in adjusting input data in any SVM and
therefore has much higher potential to improve in future
research than other midterm electricity price forecasting
methods. All of the study cases were run on a PC with 4 GB
of RAM and a 2.4 GHz processor. MATLAB 7.7 is used. The
average forecasting time is less than 1 minute.
3.3. Discussions. The SVM intends to lose the top and the
bottom peak values during training process because most of
those values are considered as nonsupport vectors when utilizing the 𝜀-insensitive loss function with 2𝜀 bandwidth. Only
the support vectors are used to create the 2𝜀 tube and only the
values outside the 2𝜀 tube are considered during simulation.
As mentioned before, the electricity MCP in the peak price
zone is mainly determined by business competing strategy
and even unethical business behaviour and those elements
cannot be easily represented mathematically. Therefore, when
using a single SVM forecasting model, the forecast electricity
MCP will lose most of its top and bottom peak values during
the forecasting process. The proposed two-stage multiple
SVM forecasting model can improve the compromise that
is caused by using a single SVM by distributing the initially
Journal of Energy
9
Table 8: Performance evaluation results between the proposed two-stage multiple SVM model and other forecasting models.
June 2009
MAPE
11.7491
10.9722
10.6706
10.7466
11.4083
MAE
2.9743
2.8152
2.7630
2.7811
2.9625
Single SVM
Single LSSVM
Hybrid LSSVM and ARMAX
Multiple LSSVM
Two-stage multiple SVM
MAE
7.2523
7.9003
7.0989
7.0950
6.8106
June 2010
MAPE
15.6454
16.2610
13.9709
13.2850
14.6567
MSRE
0.3316
0.3964
0.3859
0.3733
0.3126
the price forecasting module also have the flexibility of using
different dimensions of input data to achieve the optimal
results. Future research will focus on possible modules that
can be added to the distribution module to improve the
system accuracy.
140
Electricity MCP ($/MWh)
MSRE
0.1564
0.1513
0.1495
0.1463
0.1536
120
100
80
Conflict of Interests
60
The authors declare that there is no conflict of interests
regarding the publication of this paper.
40
20
0
100
200
300
400
Hour
500
600
700
Real MCP
Single SVM forecast MCP
Two-stage multiple SVM forecast MCP
Figure 5: Forecasted electricity MCP in June 2010 using both single
and two-stage multiple SVM.
predicted price values into different price zones. By doing
so, instead of having only two control parameters in a single
SVM forecasting model, the proposed two-stage multiple
SVM forecasting model has 10 control parameters that can
be adjusted to optimize the system forecasting accuracy.
4. Conclusions
A two-stage multiple SVM based midterm forecasting model
of the electricity MCP is proposed in this paper. Two modules, input data distribution module and price forecasting
module, are designed to first preprocess the initially predicted
price values into corresponding price zones and then forecast
the electricity price in four parallel designed SVMs. The
proposed two-stage multiple SVM model showed improved
forecasting accuracy in the low and the peak price zones and
thus improving the overall forecasting accuracy compared
to the forecasting model utilizing a single SVM. The case
studies also show that the performance of either a single
or a two-stage multiple SVM is highly depending on the
selection of the input data. Carefully selected training input
data and correctly predicted subdata sets would significantly
improve the accuracy of the forecasting model. The proposed
forecasting model has ten adjustable control parameters
compared to only two adjustable control parameters in a
single SVM forecasting model. The four parallel SVMs in
References
[1] S. S. Torbaghan, A. Motamedi, H. Zareipour, and L. A. Tuan,
“Medium-term electricity price forecasting,” in Proceedings of
the North American Power Symposium (NAPS '12), pp. 1–8,
Champaign, Ill, USA, September 2012.
[2] X. Yan, Electricity market clearing price forecasting in a deregulated electricity market [M.S. dissertation], Department of Electrical and Computer Engineering, University of Saskatchewan,
2009.
[3] X. Yan and N. A. Chowdhury, “Electricity market clearing price
forecasting in a deregulated electricity market,” in Proceedings of
the IEEE 11th International Conference on Probabilistic Methods
Applied to Power Systems (PMAPS ’10), pp. 36–41, IEEE, Singapore, June 2010.
[4] X. Yan and N. A. Chowdhury, Electricity Market Clearing
Price Forecasting in a Deregulated Market: A Neural Network
Approach, VDM, Saarbrücken, Germany, 2010.
[5] S. S. Torghaban, H. Zareipour, and L. A. Tuan, “Medium-term
electricity market price forecasting: a data-driven approach,” in
Proceedings of the North American Power Symposium (NAPS
’10), pp. 1–7, Arlington, Va, USA, September 2010.
[6] J. Contreras, R. Espı́nola, F. J. Nogales, and A. J. Conejo,
“ARIMA models to predict next-day electricity prices,” IEEE
Transactions on Power Systems, vol. 18, no. 3, pp. 1014–1020,
2003.
[7] S. J. Yao and Y. H. Song, “Prediction of system marginal prices
by wavelet transform and neural network,” in Proceedings of the
Electric Machines and Power Systems, pp. 983–993, 2000.
[8] C.-I. Kim, I.-K. Yu, and Y. H. Song, “Prediction of system
marginal price of electricity using wavelet transform analysis,”
Energy Conversion and Management, vol. 43, no. 14, pp. 1839–
1851, 2002.
[9] J. L. Zhang and Z. F. Tan, “Day-ahead electricity price forecasting using WT, CLSSVM and EGARCH model,” International
Journal of Electrical Power and Energy Systems, vol. 45, no. 1, pp.
362–368, 2013.
10
[10] C. M. Ruibal and M. Mazumdar, “Forecasting the mean and
the variance of electricity prices in deregulated markets,” IEEE
Transactions on Power Systems, vol. 23, no. 1, pp. 25–32, 2008.
[11] Z. Obradovic and K. Tomsovic, “Time series methods for
forecasting electricity market pricing,” in Proceedings of the
IEEE Power Engineering Society Summer Meeting, vol. 2, pp.
1264–1265, Edmonton, Canada, 1999.
[12] J. Crespo Cuaresma, J. Hlouskova, S. Kossmeier, and M.
Obersteiner, “Forecasting electricity spot-prices using linear
univariate time-series models,” Applied Energy, vol. 77, no. 1, pp.
87–106, 2004.
[13] F. J. Nogales, J. Contreras, A. J. Conejo, and R. Espı́nola,
“Forecasting next-day electricity prices by time series models,”
IEEE Transactions on Power Systems, vol. 17, no. 2, pp. 342–348,
2002.
[14] F. Gao, X. H. Guan, X.-R. Cao, and A. Papalexpoulos, “Forecasting power market clearing price and quantity using a neural
network method,” in Proceedings of the IEEE Power Engineering
Society Summer Meeting, vol. 4, pp. 2183–2188, Seattle, Wash,
USA, July 2000.
[15] J. P. S. Catalão, S. J. P. S. Mariano, V. M. F. Mendes, and L. A.
F. M. Ferreira, “Short-term electricity prices forecasting in a
competitive market: a neural network approach,” Electric Power
Systems Research, vol. 77, no. 10, pp. 1297–1304, 2007.
[16] P. S. Georgilakis, “Market clearing price forecasting in deregulated electricity markets using adaptively trained neural networks,” in Proceedings of the 4th Helenic Conference on Artificial
Intelligence, pp. 56–66, Heraklion, Greece, May 2006.
[17] Z. Xu, Z. Y. Dong, and W. Liu, “Neural network models for
electricity market forecasting,” in Neural Networks Applications
in Information Technology and Web Engineering, D. Wang and
N. K. Lee, Eds., pp. 233–245, Borneo Publishing Corporation,
Sarawak, Malaysia, 1st edition, 2005.
[18] D. Singhal and K. S. Swarup, “Electricity price forecasting using
artificial neural networks,” International Journal of Electrical
Power and Energy Systems, vol. 33, no. 3, pp. 550–555, 2011.
[19] S. Anbazhagan and N. Kumarappan, “Day-ahead deregulated
electricity market price classification using neural network
input featured by DCT,” International Journal of Electrical Power
and Energy Systems, vol. 37, no. 1, pp. 103–109, 2012.
[20] W. Sun, J.-C. Lu, and M. Meng, “Application of time series based
SVM model on next-day electricity price forecasting under
deregulated power market,” in Proceedings of the International
Conference on Machine Learning and Cybernetics, pp. 2373–
2378, August 2006.
[21] D. M. Zhou, F. Gao, and X. H. Guan, “Application of accurate
online support vector regression in energy price forecast,” in
Proceedings of the 5th World Congress on Intelligent Control and
Automation (WCICA ’04), pp. 1838–1842, June 2004.
[22] L. L. Hu, G. Taylor, H. B. Wan, and M. Irving, “A review of shortterm electricity price forecasting techniques in deregulated
electricity markets,” in Proceedings of the 44th International
Universities Power Engineering Conference, pp. 1–5, September
2009.
[23] R. A. Swief, Y. G. Hegazy, T. S. Abdel-Salam, and M. A. Bader,
“Support vector machines (SVM) based short term electricity
load-price forecasting,” in Proceedings of the IEEE Bucharest
PowerTech, pp. 1–5, Bucharest, Romania, June 2009.
[24] L. M. Saini, S. K. Aggarwal, and A. Kumar, “Parameter optimisation using genetic algorithm for support vector machinebased price-forecasting model in National electricity market,”
Journal of Energy
IET Generation, Transmission & Distribution, vol. 4, no. 1, pp.
36–49, 2010.
[25] W. Sun and J. Zhang, “Forecasting day ahead spot electricity
prices based on GASVM,” in Proceedings of the International
Conference on Internet Computing in Science and Engineering
(ICICSE ’08), pp. 73–78, Harbin, China, January 2008.
[26] Y.-G. Chen and G. W. Ma, “Electricity price forecasting based
on support vector machine trained by genetic algorithm,” in
Proceedings of the 3rd International Symposium on Intelligent
Information Technology Application (IITA ’09), vol. 2, pp. 292–
295, November 2009.
[27] M. J. Mahjoob, M. Abdollahzade, and R. Zarringhalam, “GA
based optimized LS-SVM forecasting of short term electricity
price in competitive power markets,” in Proceedings of the
3rd IEEE Conference on Industrial Electronics and Applications
(ICIEA ’08), pp. 73–78, June 2008.
[28] D.-S. Gong, J.-X. Che, J.-Z. Wang, and J.-Z. Liang, “Short-term
electricity price forecasting based on novel SVM using artificial
fish swarm algorithm under deregulated power,” in Proceedings
of the 2nd International Symposium on Intelligent Information
Technology Application, pp. 85–89, December 2008.
[29] H. Zheng, L. Z. Zhang, L. Xie, and X. Li, “SVM model of system
marginal price based on developed independent component
analysis,” in Proceedings of the International Conference on
Power System Technology, pp. 1437–1440, 2004.
[30] Y. Wang and S. Q. Yu, “Price forecasting by ICA-SVM in the
competitive electricity market,” in Proceedings of the 3rd IEEE
Conference on Industrial Electronics and Applications (ICIEA
’08), pp. 314–319, Singapore, June 2008.
[31] J. Y. Tian and Y. Lin, “Short-term electricity price forecasting
based on rough sets and improved SVM,” in Proceedings of the
2nd International Workshop on Knowledge Discovery and Data
Mining (WKKD ’09), pp. 68–71, IEEE, Moscow, Russia, January
2009.
[32] T. Wang and L. Qin, “Application of SVM based on rough set
in electricity prices forecasting,” in Proceedings of the 2nd Conference on Environmental Science and Information Application
Technology (ESIAT ’10), pp. 317–320, IEEE, Wuhan, China, July
2010.
[33] L. Xie, H. Zheng, and L. Z. Zhang, “Electricity price forecasting
by clustering-LSSVM,” in Proceedings of the 8th International
Power Engineering Conference, pp. 697–702, December 2007.
[34] S. Fan, J. R. Liao, K. Kaneko, and L. N. Chen, “An integrated
machine learning model for day-ahead electricity price forecasting,” in Proceedings of the IEEE PES Power Systems Conference and Exposition (PSCE ’06), pp. 1643–1649, November 2006.
[35] S. Fan, C. Mao, and L. Chen, “Next-day electricity-price forecasting using a hybrid network,” IET Generation, Transmission
and Distribution, vol. 1, no. 1, pp. 176–182, 2007.
[36] J. H. Zhao, Z. Y. Dong, Z. Xu, and K. P. Wong, “A statistical
approach for interval forecasting of the electricity price,” IEEE
Transactions on Power Systems, vol. 23, no. 2, pp. 267–276, 2008.
[37] J. H. Zhao, Z. Y. Dong, X. Li, and K. P. Wong, “A general method
for electricity market price spike analysis,” in Proceedings of the
IEEE Power Engineering Society General Meeting, pp. 286–293,
June 2005.
[38] J. H. Zhao, Z. Y. Dong, X. Li, and K. P. Wong, “A framework
for electricity price spike analysis with advanced data mining
methods,” IEEE Transactions on Power Systems, vol. 22, no. 1,
pp. 376–385, 2007.
Journal of Energy
[39] P. Areekul, T. Senjyu, H. Toyama, and A. Yona, “A hybrid
ARIMA and neural network model for short-term price forecasting in deregulated market,” IEEE Transactions on Power
Systems, vol. 25, no. 1, pp. 524–530, 2010.
[40] L. Xie, L. Z. Zhang, H. Zheng, and Y. Xie, “On the sensitivity
analysis of electricity price,” in Proceedings of the 2nd IEEE
Conference on Industrial Electronics and Applications, pp. 1603–
1606, May 2007.
[41] Y. Wang, “Price-load elasticity analysis by hybrid algorithm,” in
Proceedings of the 3rd International Conference on Electric Utility
Deregulation and Restructuring and Power Technologies (DRPT
’08), pp. 233–237, IEEE, Nanjing, China, April 2008.
[42] H. M. I. Pousinho, V. M. F. Mendes, and J. P. S. Catalão, “Shortterm electricity prices forecasting in a competitive market
by a hybrid PSO-ANFIS approach,” International Journal of
Electrical Power and Energy Systems, vol. 39, no. 1, pp. 29–35,
2012.
[43] X. Yan and N. A. Chowdhury, “Mid-term electricity market
clearing price forecasting: a hybrid LSSVM and ARMAX
approach,” International Journal of Electrical Power & Energy
Systems, vol. 53, no. 1, pp. 20–26, 2013.
[44] D. J. Pedregal and J. R. Trapero, “Mid-term hourly electricity
forecasting based on a multi-rate approach,” Energy Conversion
and Management, vol. 51, no. 1, pp. 105–111, 2010.
[45] J. G. González, J. Barquı́n, and P. Dueñas, “A hybrid approach
for modeling the electricity price series in the medium term,”
in Proceedings of the Power Systems Computation Conference
(PSCC ’08), 2008.
[46] C. Cortes and V. Vapnik, Support-Vector Networks, AT&T Bell
Labs, Holmdel, NJ, USA, 1995.
[47] Electricity LMP in PJM, 2014, http://www.pjm.com/marketsand-operations/energy/day-ahead/lmpda.aspx.
[48] Federal Energy Regulatory Commission, 2010, http://www.ferc
.gov/.
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